Addition of orography to the semi-implicit version of the Shuman-Hovermale Model

"The semi-implicit time integration scheme has been reported in the literature for several years and is used in a number of multilayer numerical weather prediction models around the globe. The implicit treatment permits a long time-step to be used in a forecast model because it time-averages terms in the equations which govern the fastest moving gravity waves. All other terms are treated in the normal explicit sense. The computation time savings resulting from the long time-step make the semi-implicit technique particularly attractive for numerical models that are being used in an operational forecasting environment. Because a set of Helmholtz equations must be solved during each time step, the savings from the semi-implicit method is not so great as would be expected from the longer time step. However, computation time savings of four to one are reported for a six to one ratio of time step lengths in semi-implicit versus explicit runs"--Introduction. Kenneth A. Campana. "June 1977." "This is an unreviewed manuscript, primarily intended for informal exchange of information among NMC staff members." System requirements: Adobe Acrobat Reader. Includes bibliographical references (page 9). 1977 NWS (National Weather Service) Library Public Domain 1931